Asymptotic time behavior of correlation functions. II. Kinetic and potential terms

Nonequilibrium Casimir-like Forces in Liquid Mixtures

“…In thin fluid layers, fluctuations not only may induce a force on the walls, but also may introduce an effective potential inside the fluid layer causing a modification of the density or composition profile [15]. While in a one-component fluid nonequilibrium fluctuations induce the latter phenomenon yielding a rearrangement of the density profile [16], the purpose of the present Letter is to demonstrate that nonequilibrium concentration fluctuations induce an actual Casimir pressure on the walls directly.It is well known that in considering the dynamics of fluctuations around thermal equilibrium, nonlinear terms in the hydrodynamic equations serve to renormalize various terms in the linearized hydrodynamic equations [17][18][19][20][21][22][23][24].Here we show that in a NESS the nonlinear terms cause a most important renormalization of the nonequilibrium (NE) pressure or normal stresses in a binary fluid. To determine the nonequilibrium induced pressure in a liquid mixture, we need to consider the pressure p as a function of the fluctuating conserved quantities, which are the fluctuating energy density e þ δe, the fluctuating mass densities ρ 1 þ δρ 1 , and ρ 2 þ δρ 2 of components 1 (solute) and 2 (solvent).…”

“…It is well known that in considering the dynamics of fluctuations around thermal equilibrium, nonlinear terms in the hydrodynamic equations serve to renormalize various terms in the linearized hydrodynamic equations [17][18][19][20][21][22][23][24].…”

Fluctuating Hydrodynamics Approach to Equilibrium Time Correlations for Anharmonic Chains

“…They also argued that the same behavior should hold for collective transport. Theory quickly jumped in and predicted a decay as t −d/2 for viscosity and thermal conductivity [5,6]. There are several theoretical schemes and they all arrive at the same prediction, which of course increases their confidence level.…”

“…Thus we still have to transform back to the physical fields through the R matrix. The computation can be found in [70] with the result 6) where {ψ α } are the eigenvectors of A, Aψ 0 = 0, Aψ 1 = cψ 1 , see [29]. If (4.33) is satisfied, e.g.…”

“…For one-dimensional fluids, van Beijeren [36] follows the scheme developed in [6] and arrived first at the prediction (4.2) together with the Lévy 5/3 heat peak to be discussed below. In [36] no Langevin equations appear.…”